# How do you find the domain and range of root5(-4-7x)?

Jun 21, 2018

See below

#### Explanation:

This is an odd number root, so negative values for the radicand are allowed. Therefore domain is:

$\left\{x \in \mathbb{R}\right\}$

or

$\left(- \infty , \infty\right)$

For the range we observe what happens as x goes to $\pm \infty$

as: $x \to \infty$ , $\textcolor{w h i t e}{8888} - 4 - 7 x \to - \infty$

as: $x \to - \infty$ , $\textcolor{w h i t e}{8888} - 4 - 7 x \to \infty$

Therefore the range is:

$\left\{f \left(x\right) \in \mathbb{R}\right\}$

or

$\left(- \infty , \infty\right)$

The graph of $f \left(x\right) = \sqrt[5]{- 4 - 7 x}$ confirms this:

graph{y=root(5)(-4-7x) [-10, 10, -5, 5]}